Thanks for your response. After a lot of research I've found what I want to do is not possible. I'm now looking at other options such as Nakama or rolling my own server using PHP, Ruby, or Node.js. For now I'll just run a simple GDScript server app on another PC on my local network.
My biggest challenge is getting Godot to talk to a database since there is no built-in support for it. That makes a server written in GDScript pretty much useless for a full scale roll-out of my game.